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Asymptotic behavior of the Weber location problem on the plane

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Abstract

The asymptotic behavior of the Weber location problem is investigated. We consider problems wheren demand points are randomly generated in a unit disk by a uniform distribution and all weights are equal to one. The main result of the paper is that the probability that the optimal solution be on a demand point is approximately 1/n. Additional results for a largen: the optimal solution converges almost surely to the center of the disk; the difference between the optimal value of the objective function and the minimal value of the objective function on a demand point converges to 1/2.

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Authors and Affiliations

  1. Department of Management Science, School of Business Administration and Economics, California State University, 92634, Fullerton, CA, USA

    Zvi Drezner

  2. Department of Industrial Engineering and Operations Research, Columbia University, 10027, New York, NY, USA

    David Simchi-Levi

Authors
  1. Zvi Drezner
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  2. David Simchi-Levi
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Drezner, Z., Simchi-Levi, D. Asymptotic behavior of the Weber location problem on the plane. Ann Oper Res 40, 163–172 (1992). https://doi.org/10.1007/BF02060475

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  • DOI: https://doi.org/10.1007/BF02060475

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